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arXiv · 1702.05118

Entropy, noncollapsing, and a gap theorem for ancient solutions to the Ricci flow

Yongjia Zhang
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Abstract

In this paper we discuss the asymptotic entropy for ancient solutions to the Ricci flow. We prove a gap theorem for ancient solutions, which could be regarded as an entropy counterpart of Yokota's work. In addition, we prove that under some assumptions on one time slice of a complete ancient solution with nonnegative curvature operator, finite asymptotic entropy implies kappa-noncollapsing on all scales. This provides an evidence for Perelman's more general assertion that on a complete ancient solution with nonnegative curvature operator, bounded entropy is equivalent to kappa-noncollapsing.

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Yongjia Zhang. 2017-02-16. Entropy, noncollapsing, and a gap theorem for ancient solutions to the Ricci flow. https://arxiv.org/abs/1702.05118

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